A large plastic prism is put into orbit somewhere the solar system. The prism reflects it's colorful rainbow into Earth's atmosphere. Thus: The Plastic Planetary Prism.

Maybe the prism will be in orbit around the sun like our planet is, so that the rainbow affects Earth only once per year and at a
short time indeed.

Or maybe in orbit around Earth itself? Imagine: It's sundown, the sun is setting, you look to the sky, and oh-what's this? The PPP is coming around the Earth's terminator directing a beautiful rainbow across the sky!

Maybe another one could be placed orbiting the moon, so that at night, you could see the moon light up with dozens of colors!

I agree: rainbows are way too beautiful to just be seen so
rarely. So, if you're into making an "human generated"
rainbow, there should be a way for it to be permanent!

Now that I think about it, making it permanent will make
it lose some of its charm... just make it show up rarely
enough so we don't get used to it, but often enough so
putting a PPP out there is worth the cost.

You can actually get this effect with high altitude ice crystals. I have photos somewhere, but I'm not sure I can lay my hands on them quickly.

But unless you're throwing the prism's light onto thin clouds, all you're going to see is a flash of colored light - try looking into a prism directed at the sun (with dark glasses on, for safety's sake).

As for the moon, the bright side is illuminated with bright direct sunlight - I'm not sure you could get nearly enough prismed light onto it to show up this far away.

And the dark side is already lit up by the Earth: this is so dim you can only see it when there is a lunar eclipse. Again, I doubt you will manage anything brighter.

The PPPs already exist in a natural state
and are called raindrops! :D
Of course you need many of them, since
you'll only catch a little bit of the light
spectrum that each emits. Add up the
inputs of all those drops and, lo! and
behold, a rainbow appears.
A single prism won't generate a rainbox
for any observer looking up at it, just a
single color.

//The PPPs already exist in a natural state and are called raindrops!// - Could we make space-clouds? What happens to water in space? Is it so cold that it freezes, or does it boil due to the lack of pressure?

// What happens to water in space? // I
would think that if it doesn't freeze very
quickly, it disperses, unless we are
talking about huge bodies of water
which generate enough gravity to retain
its particles.